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arXiv · 2606.15249

A universal support theorem for 1-Wasserstein optimal transport

Ze-An Ng
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Abstract

We show that every optimal transport plan for the $1$-Wasserstein distance in $\mathbb R^n$ is supported on a closed $n+1$ rectifiable set. In particular, the support of any optimal plan has Hausdorff dimension at most $n+1$.

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Ze-An Ng. 2026-06-13. A universal support theorem for 1-Wasserstein optimal transport. https://arxiv.org/abs/2606.15249

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